IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

prakhar_galaxy

Hi

bhaiya

actually i am nowadays doing 3-d in maths

i am doing it from 12th R D Sharma .But i am very much confused between direction ratios & direction cosines

Although thoda thoda to clear ho raha hai but zyada accha samajh mein nahin aaya

so plz tell wat actually these 2 things r

Secondly,as i hav read dat direction cosines r fixed for a particular vector but direction ratios can hav infinte set of values

So if there is an eqn of vector: 3i+6j+9k

then we will take it's direction ratios as 3,6,9 or 1,2,3

plz bro help me

these 2 things ofrm basic of whole 3-d

ok

hoping for quick reply

iitjee08aspirant

take the ratios as 1,2,3 as ther r RATIOS

sboosy

as the name suggests direction ratio is actually a ratio which means it is very much understandable when it takes different values

example:

ai+bj+ck

DR's can be a b c or 2a 2b 2c or any multiple of the same

now Direction cosines take a fixed value for a given line

this is also understandable because

given ai+bj+ck

DC= a/

(a²+b²+c²), b/

(a²+b²+c²),c/

(a²+b²+c²)

now replacing a b c by ka kb kc the above ratio is unaltered thus we see that there is a fixed DC for a given line

iitkgp_bipin

Direction cosine is a specific case of direction ratio.

Direction cosine is unique for a vector. If l.m.n are direction cosines then they must follow the relation : l²+m²+n² = 1

If a,b,c are direction ratios they can take values as per : a:b:c = l:m:n

For 3i+6j+9k : 3,6,9 and 1,2,3 both represent direction ratios but we generally write them in their simplest form which is 1,2,3.

In all direction ratios can take multiple values but their ratio is constant for a given vector.

prakhar_galaxy

thanx bhaiya
also thanx to mohit & sboosy

Ask & Discuss Questions with Community & Experts